lijiext
/
lammps
mirror of https://github.com/lammps/lammps.git
1
0
Fork 1
Code Issues Packages Projects Releases Wiki Activity

git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@4127 f3b2605a-c512-4ea7-a41b-209d697bcdaa

This commit is contained in:
sjplimp 2010-05-14 15:10:38 +00:00
parent 6cb8c3d249
commit 62eebd90af
5 changed files with 62 additions and 56 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

4
doc/Manual.html
View File

@ -149,6 +149,8 @@ listed above.
4.16 <A HREF = "Section_howto.html#4_16">Thermostatting, barostatting, and compute temperature</A>
<BR>
4.17 <A HREF = "Section_howto.html#4_17">Walls</A>
<BR>
4.18 <A HREF = "Section_howto.html#4_18">Elastic constants</A>
<BR></UL>
<LI><A HREF = "Section_example.html">Example problems</A>
@ -253,6 +255,8 @@ listed above.

4
doc/Manual.txt
View File

@ -106,7 +106,8 @@ listed above.
4.14 "Extended spherical and aspherical particles"_4_14 :b
4.15 "Output from LAMMPS (thermo, dumps, computes, fixes, variables)"_4_15 :b
4.16 "Thermostatting, barostatting, and compute temperature"_4_16 :b
4.17 "Walls"_4_17 :ule,b
4.17 "Walls"_4_17 :b
4.18 "Elastic constants"_4_18 :ule,b
"Example problems"_Section_example.html :l
"Performance & scalability"_Section_perf.html :l
"Additional tools"_Section_tools.html :l
@ -159,6 +160,7 @@ listed above.
:link(4_15,Section_howto.html#4_15)
:link(4_16,Section_howto.html#4_16)
:link(4_17,Section_howto.html#4_17)
:link(4_18,Section_howto.html#4_18)
:link(9_1,Section_errors.html#9_1)
:link(9_2,Section_errors.html#9_2)

2
doc/Section_example.html
View File

@ -30,7 +30,7 @@ Site</A>.
</P>
<P>These are the sample problems in the examples sub-directories:
</P>
<DIV ALIGN=center><TABLE WIDTH="0%" BORDER=1 >
<DIV ALIGN=center><TABLE BORDER=1 >
<TR><TD >colloid</TD><TD > big colloid particles in a small particle solvent, 2d system</TD></TR>
<TR><TD >crack</TD><TD > crack propagation in a 2d solid</TD></TR>
<TR><TD >dipole</TD><TD > point dipolar particles, 2d system</TD></TR>

56
doc/Section_howto.html
View File

@ -1025,7 +1025,7 @@ discussed below, it can be referenced via the following bracket
notation, where ID in this case is the ID of a compute. The leading
"c_" would be replaced by "f_" for a fix, or "v_" for a variable:
</P>
<DIV ALIGN=center><TABLE WIDTH="0%" BORDER=1 >
<DIV ALIGN=center><TABLE BORDER=1 >
<TR><TD >c_ID </TD><TD > entire scalar, vector, or array</TD></TR>
<TR><TD >c_ID[I] </TD><TD > one element of vector, one column of array</TD></TR>
<TR><TD >c_ID[I][J] </TD><TD > one element of array
@ -1198,7 +1198,7 @@ data and scalar/vector/array data.
input, that could be an element of a vector or array. Likewise a
vector input could be a column of an array.
</P>
<DIV ALIGN=center><TABLE WIDTH="0%" BORDER=1 >
<DIV ALIGN=center><TABLE BORDER=1 >
<TR><TD >Command</TD><TD > Input</TD><TD > Output</TD><TD ></TD></TR>
<TR><TD ><A HREF = "thermo_style.html">thermo_style custom</A></TD><TD > global scalars</TD><TD > screen, log file</TD><TD ></TD></TR>
<TR><TD ><A HREF = "dump.html">dump custom</A></TD><TD > per-atom vectors</TD><TD > dump file</TD><TD ></TD></TR>
@ -1448,36 +1448,36 @@ frictional walls, as well as triangulated surfaces.
<A NAME = "4_18"></A><H4>4.18 Elastic constants
</H4>
<P>Elastic constants characterize the stiffness of a material. The formal
definition is provided by the linear relation that holds between
the stress and strain tensors in the limit of infinitesimal deformation.
In tensor notation, this is expressed as s_ij = C_ijkl * e_kl, where
definition is provided by the linear relation that holds between the
stress and strain tensors in the limit of infinitesimal deformation.
In tensor notation, this is expressed as s_ij = C_ijkl * e_kl, where
the repeated indices imply summation. s_ij are the elements of the
symmetric stress tensor. e_kl are the elements of the symmetric
strain tensor. C_ijkl are the elements of the fourth rank tensor
of elastic constants. In three dimensions, this tensor has 3^4=81
elements. Using Voigt notation, the tensor can be written
as a 6x6 matrix, where C_ij is now the derivative of s_i
w.r.t. e_j. Because s_i is itself a derivative w.r.t. e_i, it follows
that C_ij is also symmetric, with at most 6*5/2 = 21 distinct elements.
symmetric stress tensor. e_kl are the elements of the symmetric strain
tensor. C_ijkl are the elements of the fourth rank tensor of elastic
constants. In three dimensions, this tensor has 3^4=81 elements. Using
Voigt notation, the tensor can be written as a 6x6 matrix, where C_ij
is now the derivative of s_i w.r.t. e_j. Because s_i is itself a
derivative w.r.t. e_i, it follows that C_ij is also symmetric, with at
most 6*5/2 = 21 distinct elements.
</P>
<P>At zero temperature, it is easy to estimate these derivatives by
deforming the cell in one of the six directions using
the command <A HREF = "displace_box.html">displace_box</A>
and measuring the change in the stress tensor. A general-purpose
script that does this is given in the examples/elastic directory
described in <A HREF = "Section_example.html">this section</A>.
deforming the cell in one of the six directions using the command
<A HREF = "displace_box.html">displace_box</A> and measuring the change in the
stress tensor. A general-purpose script that does this is given in the
examples/elastic directory described in <A HREF = "Section_example.html">this
section</A>.
</P>
<P>Calculating elastic constants at finite temperature is more challenging,
because it is necessary to run a simulation that perfoms time averages
of differential properties. One way to do this is to measure the change in
average stress tensor in an NVT simulations when the cell volume undergoes a
finite deformation. In order to balance
the systematic and statistical errors in this method, the magnitude of the
deformation must be chosen judiciously, and care must be taken to fully
equilibrate the deformed cell before sampling the stress tensor. Another
approach is to sample the triclinic cell fluctuations that occur in an
NPT simulation. This method can also be slow to converge and requires
careful post-processing <A HREF = "#Shinoda">(Shinoda)</A>
<P>Calculating elastic constants at finite temperature is more
challenging, because it is necessary to run a simulation that perfoms
time averages of differential properties. One way to do this is to
measure the change in average stress tensor in an NVT simulations when
the cell volume undergoes a finite deformation. In order to balance
the systematic and statistical errors in this method, the magnitude of
the deformation must be chosen judiciously, and care must be taken to
fully equilibrate the deformed cell before sampling the stress
tensor. Another approach is to sample the triclinic cell fluctuations
that occur in an NPT simulation. This method can also be slow to
converge and requires careful post-processing <A HREF = "#Shinoda">(Shinoda)</A>
</P>
<HR>

52
doc/Section_howto.txt
View File

@ -1437,36 +1437,36 @@ frictional walls, as well as triangulated surfaces.
4.18 Elastic constants :link(4_18),h4
Elastic constants characterize the stiffness of a material. The formal
definition is provided by the linear relation that holds between
the stress and strain tensors in the limit of infinitesimal deformation.
In tensor notation, this is expressed as s_ij = C_ijkl * e_kl, where
definition is provided by the linear relation that holds between the
stress and strain tensors in the limit of infinitesimal deformation.
In tensor notation, this is expressed as s_ij = C_ijkl * e_kl, where
the repeated indices imply summation. s_ij are the elements of the
symmetric stress tensor. e_kl are the elements of the symmetric
strain tensor. C_ijkl are the elements of the fourth rank tensor
of elastic constants. In three dimensions, this tensor has 3^4=81
elements. Using Voigt notation, the tensor can be written
as a 6x6 matrix, where C_ij is now the derivative of s_i
w.r.t. e_j. Because s_i is itself a derivative w.r.t. e_i, it follows
that C_ij is also symmetric, with at most 6*5/2 = 21 distinct elements.
symmetric stress tensor. e_kl are the elements of the symmetric strain
tensor. C_ijkl are the elements of the fourth rank tensor of elastic
constants. In three dimensions, this tensor has 3^4=81 elements. Using
Voigt notation, the tensor can be written as a 6x6 matrix, where C_ij
is now the derivative of s_i w.r.t. e_j. Because s_i is itself a
derivative w.r.t. e_i, it follows that C_ij is also symmetric, with at
most 6*5/2 = 21 distinct elements.
At zero temperature, it is easy to estimate these derivatives by
deforming the cell in one of the six directions using
the command "displace_box"_displace_box.html
and measuring the change in the stress tensor. A general-purpose
script that does this is given in the examples/elastic directory
described in "this section"_Section_example.html.
deforming the cell in one of the six directions using the command
"displace_box"_displace_box.html and measuring the change in the
stress tensor. A general-purpose script that does this is given in the
examples/elastic directory described in "this
section"_Section_example.html.
Calculating elastic constants at finite temperature is more challenging,
because it is necessary to run a simulation that perfoms time averages
of differential properties. One way to do this is to measure the change in
average stress tensor in an NVT simulations when the cell volume undergoes a
finite deformation. In order to balance
the systematic and statistical errors in this method, the magnitude of the
deformation must be chosen judiciously, and care must be taken to fully
equilibrate the deformed cell before sampling the stress tensor. Another
approach is to sample the triclinic cell fluctuations that occur in an
NPT simulation. This method can also be slow to converge and requires
careful post-processing "(Shinoda)"_#Shinoda
Calculating elastic constants at finite temperature is more
challenging, because it is necessary to run a simulation that perfoms
time averages of differential properties. One way to do this is to
measure the change in average stress tensor in an NVT simulations when
the cell volume undergoes a finite deformation. In order to balance
the systematic and statistical errors in this method, the magnitude of
the deformation must be chosen judiciously, and care must be taken to
fully equilibrate the deformed cell before sampling the stress
tensor. Another approach is to sample the triclinic cell fluctuations
that occur in an NPT simulation. This method can also be slow to
converge and requires careful post-processing "(Shinoda)"_#Shinoda
:line
:line